算法题:编程实现大数的加法

叁歲伎倆 2023-07-23 03:31 16阅读 0赞

两个数相加，结果位数最大为 最大的那个数的位数+1  
比如有两个数字123 21  
当两个数的相应的位都相加，先不进位，从个位开始依次相加  
999+99= 9 18 18  
然后，再计算进位，个位变为:18-18/10=8 十位变为:(18+1)-19/10=9  
百位变为 (9+1)-10/10=0 千位变为1，结果就是1098  
然后根据该思想编写算法

package algorithm;
    
    import org.junit.Test;
    
    public class Test1 { 
    
    	
    	public static void main(String []args) { 
    		String a="2001";
    		String b="9999999";
    		char[] large=null;
    		char[] small=null;
    		if (a.length()>b.length()) { 
    			large=a.toCharArray();
    			small=b.toCharArray();			
    		} else { 
    			small=a.toCharArray();
    			large=b.toCharArray();
    		}
    		int[]sums=new int[large.length+1];//最终结果的位数，最高位为0
    		for(int i=0;i<large.length;i++) { 
    			sums[i]=large[large.length-i-1]-'0';
    			
    		}
    		/*System.out.println(); for (int i = 0; i < sums.length; i++) { System.out.print(sums[i]+" "); } System.out.println();*/
    		
    		for(int i=0;i<small.length;i++) { 
    			sums[i]+=small[small.length-i-1]-'0';
    			
    		}
    		/*System.out.println(); for (int i = 0; i < sums.length; i++) { System.out.print(sums[i]+" "); } System.out.println();*/
    		for (int i = 0; i < sums.length; i++) { 
    			if (sums[i]>=10) { //判断是否进位
    				sums[i+1]+=sums[i]/10;
    				sums[i]%=10;
    			}
    		}
    		/*System.out.println(); for (int i = 0; i < sums.length; i++) { System.out.print(sums[i]+" "); } System.out.println();*/
    		StringBuilder stringBuilder=new StringBuilder();
    		for (int i = 0; i < sums.length; i++) { 
    			stringBuilder.append(sums[sums.length-1-i]);
    		}
    		System.out.println();
    		System.out.println(stringBuilder);
    		String result=stringBuilder.toString();
    		if (result.startsWith("0")) { 
    			result=result.substring(1);	
    		}
    		System.out.println(result);
    	}
    }